Inequalities for interval-valued Riemann diamond-alpha integrals

Abstract

Abstract We propose the concept of Riemann diamond-alpha integrals for time scales interval-valued functions. We first give the definition and some properties of the interval Riemann diamond-alpha integral that are naturally investigated as an extension of interval Riemann nabla and delta integrals. With the help of the interval Riemann diamond-alpha integral, we present interval variants of Jensen inequalities for convex and concave interval-valued functions on an arbitrary time scale. Moreover, diamond-alpha Hölder’s and Minkowski’s interval inequalities are proved. Also, several numerical examples are provided in order to illustrate our main results.

Keywords

• Interval-valued functions
• Time scales
• Diamond-alpha integral
• Jensen’s inequalities
• Hölder’s inequalities
• Minkowski’s inequalities